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# How many prime numbers between 1 and 100 are factors of 7,15

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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How many prime numbers between 1 and 100 are factors of 7,15 [#permalink]

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09 Mar 2017, 17:01
elisabettaportioli wrote:
Bunuel
Bunuel wrote:
How many prime numbers between 1 and 100 are factors of 7,150 ?

(A) One
(B) Two
(C) Three
(D) Four
(E) Five

Make prime factorization of 7,150 --> $$7,150=2*5^2*11*13$$. So, 4 prime numbers between 1 and 100 (namely 2, 5, 11, and 13) are factors of 7,150.

Bunuel,

Do you have any fast tricks to understand that 7,150 is divisible by 11 and 13?

The only silly mistake I made was to miss 11 and 13 as prime factors of 7150.

Thank you!

One of the questions above is how to recognize easily if a number is a multiple of 11 or not.

Let $$N$$ be an integer $$a_m a_{m-1} ... a_2 a_1 a_0$$ written in 10 base notation.
Consider the difference between $$a_0 + a_2 + a_4 + ...$$, the sum of digits at even numbered positions such as 0th, 2nd, 4th, ... and $$a_1 + a_3 + a5 + ...$$, the sum of digits at odd numbered positions such 1st, 3rd, 5th, ... .
If $$( a_0 + a_2 + a_4 + ... ) - ( a_1 + a_3 + a5 + ... )$$ is a multiple of 11, then $$N$$ must be a multiple of 11.

Here, in this question, we have ( 7 + 5 ) - ( 1 + 0 ) = 12 - 1 = 11, which is a multiple of 11.
Thus 7150 must be a multiple of 11.

For 143, ( 1 + 3 ) - 4 is 0, which is also a multiple of 11.
Thus 143 is a multiple of 11.

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Re: How many prime numbers between 1 and 100 are factors of 7,15 [#permalink]

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12 Mar 2017, 07:12
v0latility wrote:
How many prime numbers between 1 and 100 are factors of 7,150?

A. One
B. Two
C. Three
D. Four
E. Five

I correctly factored 7,150 into 13 x 11 x 5 x 5 x 2. So there are 5 prime factors in total, 4 of which are unique. The correct answer is 4. So the GMAT must have been asking for the # of unique factors? I'm just having a little trouble convincing myself how the language in the question stem translates to unique vs. total.

You can say that again. This question is very straight forward. Except for the language in the question stem that will certainly trick many people.
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Director
Joined: 02 Sep 2016
Posts: 744
Re: How many prime numbers between 1 and 100 are factors of 7,15 [#permalink]

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03 Apr 2017, 04:43
FACTORIZE 7150

7150= 715*10= 5*11*13*2*5

In exponential form:
7150= 2*5^2*11*13

Four prime factors between 1 and 100.
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Director
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Re: How many prime numbers between 1 and 100 are factors of 7,15 [#permalink]

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02 Jan 2018, 04:38
How many prime numbers between 1 and 100 are factors of 7,150 ?

(A) One
(B) Two
(C) Three
(D) Four
(E) Five

Hello Everyone Can anyone suggest divisibility rule by 7, 11, and 13 ? Thanks!
Math Expert
Joined: 02 Sep 2009
Posts: 46307
Re: How many prime numbers between 1 and 100 are factors of 7,15 [#permalink]

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02 Jan 2018, 04:50
dave13 wrote:
How many prime numbers between 1 and 100 are factors of 7,150 ?

(A) One
(B) Two
(C) Three
(D) Four
(E) Five

Hello Everyone Can anyone suggest divisibility rule by 7, 11, and 13 ? Thanks!

It's unlikely that you'll need those but you can check them here: https://gmatclub.com/forum/math-number- ... ml#p666609
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Re: How many prime numbers between 1 and 100 are factors of 7,15   [#permalink] 02 Jan 2018, 04:50

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